In 1960, Baxter [1]} introduced the notion of Rota-Baxter operators on associative algebras in his study of fluctuation theory in probability. Rota-Baxter operators have been found many applications, including in Connes-Kreimer's algebraic approach
to the renormalization in perturbative quantum field theory [2]}.
For more details on the Rota-Baxter operator, see [3]}.
